Page 374 - Water and wastewater engineering

REVERSE OSMOSIS AND NANOFILTRATION 9-13

d. This indicates that the solubility will be exceeded and no recovery is possible.

Comments:
1. As noted above, for an accurate answer, the activity must be taken into account. Recov-
ery will increase the total dissolved solids (TDS) and, in turn, increase the ionic strength.
Increasing the ionic strength increases the solubility (Taylor and Wiesner, 1999).

Example 9-2. Estimate the dose of sulfuric acid required to achieve a product water recovery
rate of 75% for the water in Example 9-1 . Assume the acid is a 100% solution.

Solution:
a. Convert the alkalinity in Example 9-1 to moles/L.

⎛ 61 g/eq HCO ⎞
(310 mg/L as CaCO ⎜ 3 ⎟ 378 2 mg/L as HCO
)
.
3
3
⎝ 50 g/eq CaCO 3 ⎠
O

.
378 2 mg/L as HCCO
3 3
62 . 10 moles/L
,
61 000 mg/mole
b. Write the second dissociation of carbonic acid in terms of the carbonate. From Appen-
dix A, the dissociation constant p K 2 is 10.33.

2 K [ HCO ]
2
3
CO
3
[ H ]
.
10 33
K 2 10
2 10 10 33. [ 6 2 . 10 3 moles/L]
CO 3
[ H ]
2

c. Substitute this expression for CO in Equation 9-13 :
3
.
⎡ 2 38 10 3 moles/L ⎤ 10 10.333 [ 62 10 3 moles/L]
.
495 10 9 ⎢ ⎥ £ [H ] §
.
⎣ 1 r ⎦
1 r
With an assumed product water recovery rate of 75%, r 0.75, and the equation may be
rewritten as
10..33 3
⎡ 2 38 10 3 moles/L ⎤ 10 [ . 62 10 moles/L]
.
495 10 9 ⎢ ⎥ £ [H ] §
.
⎣ 025 ⎦
.
. 025